Exploring Fractions

Grade Level: 3rd Grade

Curriculum Area: Operations and Algebraic Thinking (aligned to Common Core State Standards - CCSS.MATH.CONTENT.3.NF.A.1)
Objective: Students will understand the concept of fractions as part of a whole by learning to identify, model, and compare fractions using visual aids, manipulatives, and real-world examples.

---

Objectives

By the end of the 45-minute lesson, students will:

• Understand the definition of a fraction as a part of a whole.
• Identify numerator and denominator and their roles in fractions.
• Visualize fractions using manipulatives and drawings.
• Show proficiency in simple fraction comparisons.

---

Materials Needed

• Fraction circles (pre-made from colored paper or plastic manipulatives)
• A whiteboard and markers
• Large visual display of a pie chart or fraction wall
• Individual student sets of playdough
• Small bag of candy (like Skittles or M&Ms, one for each student)
• Printable fraction worksheet (1 per student)
• Exit tickets

---

Lesson Outline

1. Warm-Up Activity (5 minutes)

Goal: Activate prior knowledge about parts and wholes.

1. Begin with a fun, interactive question:
   “Who here loves pizza? What happens when we cut a pizza into slices? Can we count these slices as parts of the whole pizza?”
2. Display a large visual of a whole pizza drawn on the board. Draw lines to divide it into 4 equal parts. Ask students to guess what one part of the pizza is called, introducing the term "one-fourth."

This brief introduction connects fractions to a real-world, relatable concept.

---

2. Core Lesson (20 minutes)

Goal: Explicit teaching of the meaning of fractions using hands-on examples.

Part A: Define Fractions (5 minutes)

Write the fraction 1/4 on the board. Explain:

• The number on top is the numerator (how many parts we’re talking about).
• The number on the bottom is the denominator (how many equal parts the whole is divided into).

Ask: “What does it mean if the pizza has 8 parts, and I’ve eaten 3? How would we write that as a fraction?” Write it as 3/8, pointing to numerator and denominator as you explain.

Part B: Fractions with Manipulatives (10 minutes)

1. Hand out fraction circles to each group of students (4 groups of 6–7 kids). Have one student show what 1/2, 1/4, and 3/4 look like using the manipulatives.
2. Give students playdough and ask them to flatten it into a circle shape. Ask them to divide it into equal parts—a clear visual demonstration of fractions.
3. Walk around and provide positive reinforcement as students explore this hands-on learning activity.

Part C: Comparing Fractions (5 minutes)

Draw two fractions on the board: 1/8 and 1/4. Ask them to consider which is larger, introducing the concept of comparing fractions using visual size. Use the fraction wall or pie chart as a visual guide to explain this.

---

3. Guided Practice (10 minutes)

Candy Fractions Activity

1. Hand each student a small bag of candy (e.g., Skittles or M&Ms) and a printable fraction worksheet.
2. Ask students to:
   • Separate their candy by color and count each color (e.g., "How many red candies do you have?").
   • Write a fraction for each color (e.g., "If you have 2 red candies out of 10, write 2/10.").
   • Discuss as a group how different-sized groups use the same concept of fractions.
3. Challenge advanced learners: Ask them to simplify any fractions if the groupings allow (e.g., 2/10 simplifies to 1/5).

---

4. Independent Work (5 minutes)

Students complete a few practice problems on their fraction worksheet. Problems include:

1. Color fractions of a circle or rectangle.
2. Write the fraction shown in a simple pie chart.
3. Compare two given fractions using <, >, or =.

---

5. Wrap-Up and Exit Ticket (5 minutes)

1. Review key points using rapid-fire questions: “What’s the numerator? What’s the denominator? How can we write three pieces of candy out of ten as a fraction?”
2. Distribute an "exit ticket" slip with one question:
   • Write the fraction of your day you spent in math class (e.g., 45 minutes out of 6 hours).
3. Collect exit tickets to assess understanding.

---

Assessment

Formative: Observe students’ responses during group activities and hands-on exercises. Collect completed worksheets to check accuracy.
Summative: Use exit tickets to gauge whether students can correctly write fractions and understand numerator/denominator roles.

---

Differentiation

• For Struggling Learners: Offer simpler examples (e.g., fractions like 1/2 or 1/4) and provide one-on-one help with manipulatives.
• For Advanced Learners: Challenge them to convert improper fractions like 5/4 into mixed numbers or simplify fractions when possible.

---

Homework Extension

Ask students to find examples of fractions in their home (e.g., "What fraction of the eggs in the fridge are left in the carton?"). Bring one real-world fraction to share with the class tomorrow.

---

Teacher Reflection

• Were students engaged with the hands-on manipulatives?
• Did the candy exercise resonate with all learning levels?
• How many completed exit tickets showed mastery of the day's objective?